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A transversal property for permutation groups motivated by partial transformations

Publication . Araújo, João; Araújo, João Pedro; Bentz, Wolfram; Cameron, Peter; Spiga, Pablo

In this paper we introduce the definition of the (k, l)-universal transversal property for permutation groups, which is a refinement of the definition of k-universal transversal property, which in turn is a refine- ment of the classical definition of k-homogeneity for permutation groups. In particular, a group possesses the (2, n)-universal transversal property if and only if it is primitive; it possesses the (2, 2)-universal transversal property if and only if it is 2-homogeneous. Up to a few undecided cases, we give a classification of groups satisfying the (k, l)-universal transversal property, for k ≥ 3. Then we apply this result for studying regular semigroups of partial transformations.

2021-05-01Artigo científico

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Fundação para a Ciência e a Tecnologia

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6817 - DCRRNI ID

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UID/Multi/04621/2013